Difference between revisions of "Verification of Relativistic Components"

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<center>[[File:FnlTheta_reverse.png]][[File:MolTheta_reverse.png]]</center>
 
<center>[[File:FnlTheta_reverse.png]][[File:MolTheta_reverse.png]]</center>
  
 +
=Theta in the CM Frame=
 +
<center>[[File:FnlThetaCM_reverse.png]][[File:MolThetaCM_reverse.png]]</center>
  
 
=Momentum in the CM Frame=
 
=Momentum in the CM Frame=
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| 0  
 
| 0  
 
| -510  
 
| -510  
| 10999.1
+
| 10931.3
| 0.433025
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| -7.51848
| -0.858867
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| -3.62463
| 10999.6
+
| 10931.8
 
| 0  
 
| 0  
 
| 0  
 
| 0  
| -509.276
+
| -509.361
| 0.905324
+
| 68.5938
| -0.433025
+
| 7.51848
| 0.858867
+
| 3.62463
| 0.905366
+
| 68.597
 
| 0  
 
| 0  
 
| 0  
 
| 0  
| -509.276
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| -509.361
 
|}
 
|}
  
The particles start out with p=11000.511 GeV and have on average 11000 GeV by the time they interact
+
The particles start out with p=11000.511 MeV and have on average ~11000 MeV by the time they interact
  
 
<center>[[File:Screen_Shot_2016-02-01_at_9.30.23_PM.png]]</center>
 
<center>[[File:Screen_Shot_2016-02-01_at_9.30.23_PM.png]]</center>
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<center>[[File:Screen_Shot_2016-02-01_at_9.29.40_PM.png]]</center>
 
<center>[[File:Screen_Shot_2016-02-01_at_9.29.40_PM.png]]</center>
  
=Theta in the CM Frame=
+
 
<center>[[File:FnlThetaCM_reverse.png]][[File:MolThetaCM_reverse.png]]</center>
+
 
 +
=Conclusion=
 +
 
 +
The energy loss must be dealt with by using both momentum components from a GEANT Moller Scattering data file.  By using both components, they can be transformed to a CM Frame, then have the phi angle varied to cover 2π radians.  A quick awk search shows that there are no Moller electrons with energy over 5500 MeV. This might be able to be fixed by switching the scattered electron with the Moller electron, allowing a larger range of energy to be covered.

Latest revision as of 15:56, 4 February 2016

Setup

Verifying that the kinematics are valid, the Moller momentum from GEANT simulations are extracted using

awk '{print $16, $17, $18}' MollerScattering_NH3_Large.dat > Just_Mol_Mom.dat

Then using the kinematics equations displayed above, used to reverse calculate the scattered electron's momentum and angles. The root histograms of an incoming 11GeV electron (in blue) are overlaid with the relativistic calculations starting with the Moller electron (Reverse Moller in red) and show good agreement.


Final Momentum in the Lab Frame

FnlMom backwards.pngMolMom reverse.png

Final Thetas in the Lab Frame

FnlTheta reverse.pngMolTheta reverse.png

Theta in the CM Frame

FnlThetaCM reverse.pngMolThetaCM reverse.png

Momentum in the CM Frame

FnlMomCM reverse.pngMolMomCM reverse.png

The differences in these plots come from fact that the "Forward" plots come from a GEANT simulation in which a small amount of energy was lost traveling through the target material.

KEi Pxi Pyi Pzi xi yi z1 KEf Pxf Pyf Pzf xf yf zf KEm Pxm Pym Pzm xm ym zm
11000 0 0 11000.5 0 0 -510 10931.3 -7.51848 -3.62463 10931.8 0 0 -509.361 68.5938 7.51848 3.62463 68.597 0 0 -509.361

The particles start out with p=11000.511 MeV and have on average ~11000 MeV by the time they interact

Screen Shot 2016-02-01 at 9.30.23 PM.png


Screen Shot 2016-02-01 at 9.29.40 PM.png


Conclusion

The energy loss must be dealt with by using both momentum components from a GEANT Moller Scattering data file. By using both components, they can be transformed to a CM Frame, then have the phi angle varied to cover 2π radians. A quick awk search shows that there are no Moller electrons with energy over 5500 MeV. This might be able to be fixed by switching the scattered electron with the Moller electron, allowing a larger range of energy to be covered.